Tuesday, October 16, 2007

Scientific Notation Lesson with big numbers

SWBAT rewrite numbers in scientific notation.

Scientists have developed a shorter method to express very large numbers. This method is called scientific notation. Scientific Notation is based on powers of the base number 10.

The notation is based on powers of base number 10. The general format looks something like this:

N X 10x where N= number greater than or equal to 1 but less than 10 and x=exponent of base 10.

Placing numbers in exponential notation has several advantages.

For very large numbers and extrememly small ones, these numbers can be placed in scientific notation in order to express them in a more concise form.

In addition, numbers placed in this notation can be used in a computation with far greater ease. This last advantage was more practical before the advent of calculators and their abundance.

In scientific fields, scientific notation is still used.

Let's first discuss how we will express a number greater than 10 in such notational form.

Numbers Greater Than 10
We first want to locate the decimal and move it either right or left so that there are only one non-zero digit to its left.

The resulting placement of the decimal will produce the N part of the standard scientific notational expression.

Count the number of places that you had to move the decimal, and that would be your x, exponent.

If it is to the left as it will be for numbers greater than 10, that number of positions will equal x, the exponent, in the general expression above.

As an example, how do we place the number 2340000 in standard scientific notation?

Position the decimal so that there is only one non-zero digit to its left. In this case we end up with 2.34. We know that 2.34 has to be less than 10 and has to be greater than or equal to 1.

Count the number of positions we had to move the decimal to the left and that will be the exponent, x.

So we have: 2.34 X 106 in scientific notation.

That is how we convert from standard form to scientific notation.

Now, how do we go from scientific notation to standard form:

(1) Move decimal point to right the same amount of times your exponent tells you to.

For example, if your base ten exponential has an exponent of 5, you have to move the decimal point to the right 5 times.

That is, 5.67 x 105 is: 567000.

Good luck!! You all did a great job in class today.